test #1 statistics

Statistics

The science of collecting, organizing, analyzing, and interpreting data.

Population

The entire group of individuals or items being studied.

Sample

A subset of the population used to represent the population.

Parameter

A numerical measurement that describes a population.

Statistic

A numerical measurement that describes a sample.

Data

Facts, figures, observations, or measurements collected for analysis.

Variable

A characteristic that can take different values.

Census

A study that collects data from every member of a population.

Descriptive Statistics

Methods used to organize, summarize, and present data.

Inferential Statistics

Methods that use sample data to make conclusions about a population.

Observational Study

A study in which researchers observe subjects without influencing them.

Experiment

A study in which researchers apply a treatment and observe its effects.

Explanatory Variable

The variable that explains or predicts changes in another variable (independent variable).

Response Variable

The variable that is measured or observed (dependent variable).

Qualitative Variable

A variable that describes qualities or categories rather than numbers.

Quantitative Variable

A variable measured with numbers.

Discrete Variable

A quantitative variable with countable values.

Continuous Variable

A quantitative variable that can take any value within an interval.

Nominal Level

Data placed into categories with no meaningful order.

Ordinal Level

Data placed into categories with a meaningful order.

Interval Level

Numerical data with meaningful differences but no true zero.

Ratio Level

Numerical data with meaningful differences and a true zero.

Simple Random Sample

A sample in which every possible sample has an equal chance of being selected.

Systematic Sample

A sample selected by choosing every nth individual after a random starting point.

Stratified Sample

A sample obtained by dividing the population into groups and randomly sampling from each group.

Cluster Sample

A sample obtained by randomly selecting entire groups and studying everyone in those groups.

Convenience Sample

A sample chosen because it is easy to obtain.

Response Bias

Bias caused by the wording of questions or interviewer influence.

Nonresponse Bias

Bias that occurs when selected individuals do not respond.

Undercoverage Bias

Bias caused when some members of the population are left out.

Voluntary Response Bias

Bias that occurs when participants choose whether to respond.

Frequency Table

A table showing how often each value occurs.

Relative Frequency Table

A table showing the proportion or percentage of each value.

Bar Graph

A graph used to display qualitative data with separated bars.

Histogram

A graph used to display quantitative data with touching bars.

Pareto Chart

A bar graph with bars arranged from highest to lowest frequency.

Pie Chart

A circle graph showing how categories make up a whole.

Dot Plot

A graph displaying individual data values as dots.

Stem-and-Leaf Plot

A display that separates each value into a stem and a leaf.

Boxplot

A graph based on the five-number summary.

Distribution

The overall pattern of a dataset.

Symmetric Distribution

A distribution in which the left and right sides are approximately mirror images.

Right-Skewed Distribution

A distribution with a long tail extending to the right.

Left-Skewed Distribution

A distribution with a long tail extending to the left.

Uniform Distribution

A distribution where values occur with approximately equal frequency.

Bell-Shaped Distribution

A symmetric distribution with most data near the center.

Outlier

A value that is much larger or smaller than the rest of the data.

Gap

An interval containing no data values.

Cluster

A group of data values close together.

Center

The middle or typical value of a dataset.

Spread

How much the data values vary.

Mean

The arithmetic average of a dataset.

Median

The middle value of an ordered dataset.

Mode

The value that occurs most frequently.

Range

The difference between the maximum and minimum values.

Variance

A measure of how spread out data values are.

Standard Deviation

A measure of the average distance of data values from the mean.

Interquartile Range (IQR)

The difference between the third quartile and first quartile.

Five-Number Summary

The minimum, Q1, median, Q3, and maximum.

Quartiles

Values that divide ordered data into four equal parts.

Percentile

A value below which a certain percentage of observations fall.

Mean vs. Median

The mean is affected by outliers; the median is resistant to outliers.

Empirical Rule

For bell-shaped distributions, about 68%, 95%, and 99.7% of data fall within 1, 2, and 3 standard deviations of the mean.

Z-Score

The number of standard deviations a value is from the mean.

Positive Z-Score

Indicates a value above the mean.

Negative Z-Score

Indicates a value below the mean.

Scatterplot

A graph showing the relationship between two quantitative variables.

Correlation

The strength and direction of a linear relationship between two variables.

Positive Correlation

As one variable increases, the other tends to increase.

Negative Correlation

As one variable increases, the other tends to decrease.

No Correlation

No apparent linear relationship between variables.

Strong Correlation

Data points lie close to a line.

Weak Correlation

Data points are widely scattered.

Correlation Coefficient (r)

A number between -1 and 1 that measures the strength and direction of a linear relationship.

Coefficient of Determination (R²)

The proportion of variation in the response variable explained by the regression line.

Regression Line

The line of best fit used to predict values.

Residual

The difference between an observed value and its predicted value.

Correlation Does Not Imply Causation

A strong correlation does not prove that one variable causes another.

Probability

The likelihood that an event will occur.

Experiment (Probability)

A process that produces outcomes.

Outcome

A possible result of an experiment.

Sample Space

The set of all possible outcomes.

Event

A collection of one or more outcomes.

Complement

The event that an event does not occur.

Independent Events

Events where one does not affect the probability of the other.

Dependent Events

Events where one affects the probability of the other.

Mutually Exclusive Events

Events that cannot occur at the same time.

Addition Rule

Used to find the probability of "A or B."

Multiplication Rule

Used to find the probability of "A and B."

Conditional Probability

The probability of an event occurring given that another event has occurred.

Impossible Event

An event with probability 0.

Certain Event

An event with probability 1.

Random Variable

A numerical value assigned to an outcome of a random experiment.

Probability Distribution

A table or graph showing all possible values of a random variable and their probabilities.

Expected Value

The long-run average outcome of a probability distribution.

Discrete Probability Distribution

A probability distribution for a discrete random variable.

Binomial Experiment

A probability experiment with exactly two possible outcomes per trial that meets five conditions.

Five Conditions of a Binomial Experiment

Fixed number of trials, independent trials, two outcomes, constant probability, random variable counts successes.

Success

In a binomial experiment, the outcome of interest.

Failure

In a binomial experiment, the outcome that is not a success.